Abstract

By computational optimization of air-void cavities in metallic substrates, we show that the local density of states (LDOS) can reach within a factor of ≈10 of recent theoretical upper limits and within a factor ≈4 for the single-polarization LDOS, demonstrating that the theoretical limits are nearly attainable. Optimizing the total LDOS results in a spontaneous symmetry breaking where it is preferable to couple to a specific polarization. Moreover, simple shapes such as optimized cylinders attain nearly the performance of complicated many-parameter optima, suggesting that only one or two key parameters matter in order to approach the theoretical LDOS bounds for metallic resonators.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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S. Molesky, P. S. Venkataram, W. Jin, and A. W. Rodriguez, “Fundamental limits to radiative heat transfer: Theory,” Phys. Rev. B 101(3), 035408 (2020).
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R. E. Christiansen, J. Michon, M. Benzaouia, O. Sigmund, and S. G. Johnson, “Inverse design of nanoparticles for enhanced raman scattering,” Opt. Express 28(4), 4444–4462 (2020).
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2019 (2)

J. Michon, M. Benzaouia, W. Yao, O. D. Miller, and S. G. Johnson, “Limits to surface-enhanced raman scattering near arbitrary-shape scatterers,” Opt. Express 27(24), 35189–35202 (2019).
[Crossref]

H. Shim, L. Fan, S. G. Johnson, and O. D. Miller, “Fundamental limits to near-field optical response over any bandwidth,” Phys. Rev. X 9(1), 011043 (2019).
[Crossref]

2018 (2)

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12(11), 659–670 (2018).
[Crossref]

F. Wang, R. E. Christiansen, Y. Yu, J. Mørk, and O. Sigmund, “Maximizing the quality factor to mode volume ratio for ultra-small photonic crystal cavities,” Appl. Phys. Lett. 113(24), 241101 (2018).
[Crossref]

2017 (2)

O. D. Miller, O. Ilic, T. Christensen, M. T. H. Reid, H. A. Atwater, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Limits to the optical response of graphene and two-dimensional materials,” Nano Lett. 17(9), 5408–5415 (2017).
[Crossref]

D. G. Baranov, R. S. Savelev, S. V. Li, A. E. Krasnok, and A. Alù, “Modifying magnetic dipole spontaneous emission with nanophotonic structures,” Laser Photonics Rev. 11(3), 1600268 (2017).
[Crossref]

2016 (1)

2015 (2)

M. T. H. Reid and S. G. Johnson, “Efficient computation of power, force, and torque in bem scattering calculations,” IEEE Trans. Antennas Propag. 63(8), 3588–3598 (2015).
[Crossref]

S. Raza, S. I. Bozhevolnyi, M. Wubs, and N. A. Mortensen, “Nonlocal optical response in metallic nanostructures,” J. Phys.: Condens. Matter 27(18), 183204 (2015).
[Crossref]

2014 (1)

O. D. Miller, C. W. Hsu, M. T. H. Reid, W. Qiu, B. G. DeLacy, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Fundamental limits to extinction by metallic nanoparticles,” Phys. Rev. Lett. 112(12), 123903 (2014).
[Crossref]

2013 (5)

N. P. van Dijk, K. Maute, M. Langelaar, and F. van Keulen, “Level-set methods for structural topology optimization: a review,” Struct. Multidisc. Optim. 48(3), 437–472 (2013).
[Crossref]

T. W. Saucer and V. Sih, “Optimizing nanophotonic cavity designs with the gravitational search algorithm,” Opt. Express 21(18), 20831–20836 (2013).
[Crossref]

A. Mazaheri, H. R. Fallah, and J. Zarbakhsh, “Application of ldos and multipole expansion technique in optimization of photonic crystal designs,” Opt. Quant. Electron. 45(1), 67–77 (2013).
[Crossref]

M. Agio and D. M. Cano, “The purcell factor of nanoresonators,” Nat. Photonics 7(9), 674–675 (2013).
[Crossref]

X. Liang and S. G. Johnson, “Formulation for scalable optimization of microcavities via the frequency-averaged local density of states,” Opt. Express 21(25), 30812–30841 (2013).
[Crossref]

2011 (1)

J. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photonics Rev. 5(2), 308–321 (2011).
[Crossref]

2010 (2)

Z. Ruan and S. Fan, “Superscattering of light from subwavelength nanostructures,” Phys. Rev. Lett. 105(1), 013901 (2010).
[Crossref]

E. J. R. Vesseur, F. J. G. de Abajo, and A. Polman, “Broadband purcell enhancement in plasmonic ring cavities,” Phys. Rev. B 82(16), 165419 (2010).
[Crossref]

2007 (1)

R. E. Hamam, A. Karalis, J. D. Joannopoulos, and M. Soljačić, “Coupled-mode theory for general free-space resonant scattering of waves,” Phys. Rev. A 75(5), 053801 (2007).
[Crossref]

2006 (1)

T. A. Kelf, Y. Sugawara, R. M. Cole, J. J. Baumberg, M. E. Abdelsalam, S. Cintra, S. Mahajan, A. E. Russell, and P. N. Bartlett, “Localized and delocalized plasmons in metallic nanovoids,” Phys. Rev. B 74(24), 245415 (2006).
[Crossref]

2005 (2)

J.-D. Boissonnat and S. Oudot, “Provably good sampling and meshing of surfaces,” Graph. Model. 67(5), 405–451 (2005).
[Crossref]

K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: Radiative heat transfer, coherence properties and casimir forces revisited in the near field,” Surf. Sci. Rep. 57(3-4), 59–112 (2005).
[Crossref]

2004 (2)

G. D’Aguanno, N. Mattiucci, M. Centini, M. Scalora, and M. J. Bloemer, “Electromagnetic density of modes for a finite-size three-dimensional structure,” Phys. Rev. E 69(5), 057601 (2004).
[Crossref]

W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40(10), 1511–1518 (2004).
[Crossref]

2003 (1)

K. Joulain, R. Carminati, J.-P. Mulet, and J.-J. Greffet, “Definition and measurement of the local density of electromagnetic states close to an interface,” Phys. Rev. B 68(24), 245405 (2003).
[Crossref]

2002 (2)

J. Vučković, M. Pelton, A. Scherer, and Y. Yamamoto, “Optimization of three-dimensional micropost microcavities for cavity quantum electrodynamics,” Phys. Rev. A 66(2), 023808 (2002).
[Crossref]

M. Heinkenschloss and L. N. Vicente, “Analysis of inexact trust-region sqp algorithms,” SIAM J. Optim. 12(2), 283–302 (2002).
[Crossref]

2000 (1)

Y. Xu, R. K. Lee, and A. Yariv, “Quantum analysis and the classical analysis of spontaneous emission in a microcavity,” Phys. Rev. A 61(3), 033807 (2000).
[Crossref]

1998 (1)

O. J. F. Martin and N. B. Piller, “Electromagnetic scattering in polarizable backgrounds,” Phys. Rev. E 58(3), 3909–3915 (1998).
[Crossref]

1997 (2)

F. Wijnands, J. B. Pendry, F. J. Garcia-Vidal, P. M. Bell, P. J. Roberts, and L. M. Moreno, “Green’s functions for maxwell’s equations: application to spontaneous emission,” Opt. Quantum Electron. 29(2), 199–216 (1997).
[Crossref]

F. Wijnands, J. B. Pendry, F. J. Garcia-Vidal, P. M. Bell, P. J. Roberts, and L. M. Moreno, “Green’s functions for Maxwell’s equations: Application to spontaneous emission,” Opt. Quantum Electron. 29(2), 199–216 (1997).
[Crossref]

1994 (1)

D. A. Tortorelli and P. Michaleris, “Design sensitivity analysis: Overview and review,” Inverse Probl. Eng. 1(1), 71–105 (1994).
[Crossref]

1982 (1)

F. Palacios-Gomez, L. Lasdon, and M. Engquist, “Nonlinear optimization by successive linear programming,” Manag. Sci. 28(10), 1106–1120 (1982).
[Crossref]

Abdelsalam, M. E.

T. A. Kelf, Y. Sugawara, R. M. Cole, J. J. Baumberg, M. E. Abdelsalam, S. Cintra, S. Mahajan, A. E. Russell, and P. N. Bartlett, “Localized and delocalized plasmons in metallic nanovoids,” Phys. Rev. B 74(24), 245415 (2006).
[Crossref]

Agio, M.

M. Agio and D. M. Cano, “The purcell factor of nanoresonators,” Nat. Photonics 7(9), 674–675 (2013).
[Crossref]

Alù, A.

D. G. Baranov, R. S. Savelev, S. V. Li, A. E. Krasnok, and A. Alù, “Modifying magnetic dipole spontaneous emission with nanophotonic structures,” Laser Photonics Rev. 11(3), 1600268 (2017).
[Crossref]

Atwater, H. A.

O. D. Miller, O. Ilic, T. Christensen, M. T. H. Reid, H. A. Atwater, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Limits to the optical response of graphene and two-dimensional materials,” Nano Lett. 17(9), 5408–5415 (2017).
[Crossref]

Ba, J.

D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” (2014). Https://arxiv.org/abs/1412.6980 .

Banerjee, P. K.

P. K. Banerjee and R. Butterfield, Boundary element methods in engineering science (McGraw-Hill Book Co., 1981).

Baranov, D. G.

D. G. Baranov, R. S. Savelev, S. V. Li, A. E. Krasnok, and A. Alù, “Modifying magnetic dipole spontaneous emission with nanophotonic structures,” Laser Photonics Rev. 11(3), 1600268 (2017).
[Crossref]

Bartlett, P. N.

T. A. Kelf, Y. Sugawara, R. M. Cole, J. J. Baumberg, M. E. Abdelsalam, S. Cintra, S. Mahajan, A. E. Russell, and P. N. Bartlett, “Localized and delocalized plasmons in metallic nanovoids,” Phys. Rev. B 74(24), 245415 (2006).
[Crossref]

Baumberg, J. J.

T. A. Kelf, Y. Sugawara, R. M. Cole, J. J. Baumberg, M. E. Abdelsalam, S. Cintra, S. Mahajan, A. E. Russell, and P. N. Bartlett, “Localized and delocalized plasmons in metallic nanovoids,” Phys. Rev. B 74(24), 245415 (2006).
[Crossref]

Bell, P. M.

F. Wijnands, J. B. Pendry, F. J. Garcia-Vidal, P. M. Bell, P. J. Roberts, and L. M. Moreno, “Green’s functions for Maxwell’s equations: Application to spontaneous emission,” Opt. Quantum Electron. 29(2), 199–216 (1997).
[Crossref]

F. Wijnands, J. B. Pendry, F. J. Garcia-Vidal, P. M. Bell, P. J. Roberts, and L. M. Moreno, “Green’s functions for maxwell’s equations: application to spontaneous emission,” Opt. Quantum Electron. 29(2), 199–216 (1997).
[Crossref]

Benzaouia, M.

Bloemer, M. J.

G. D’Aguanno, N. Mattiucci, M. Centini, M. Scalora, and M. J. Bloemer, “Electromagnetic density of modes for a finite-size three-dimensional structure,” Phys. Rev. E 69(5), 057601 (2004).
[Crossref]

Boardman, A. D.

A. D. Boardman, Electromagnetic Surface Modes (Wiley-Interscience, 1982).

Boissonnat, J.-D.

J.-D. Boissonnat and S. Oudot, “Provably good sampling and meshing of surfaces,” Graph. Model. 67(5), 405–451 (2005).
[Crossref]

Bozhevolnyi, S. I.

S. Raza, S. I. Bozhevolnyi, M. Wubs, and N. A. Mortensen, “Nonlocal optical response in metallic nanostructures,” J. Phys.: Condens. Matter 27(18), 183204 (2015).
[Crossref]

Butterfield, R.

P. K. Banerjee and R. Butterfield, Boundary element methods in engineering science (McGraw-Hill Book Co., 1981).

Cano, D. M.

M. Agio and D. M. Cano, “The purcell factor of nanoresonators,” Nat. Photonics 7(9), 674–675 (2013).
[Crossref]

Capek, M.

M. Gustafsson, K. Schab, L. Jelinek, and M. Capek, “Upper bounds on absorption and scattering,” New Journal of Physics (2020).

Carminati, R.

K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: Radiative heat transfer, coherence properties and casimir forces revisited in the near field,” Surf. Sci. Rep. 57(3-4), 59–112 (2005).
[Crossref]

K. Joulain, R. Carminati, J.-P. Mulet, and J.-J. Greffet, “Definition and measurement of the local density of electromagnetic states close to an interface,” Phys. Rev. B 68(24), 245405 (2003).
[Crossref]

Centini, M.

G. D’Aguanno, N. Mattiucci, M. Centini, M. Scalora, and M. J. Bloemer, “Electromagnetic density of modes for a finite-size three-dimensional structure,” Phys. Rev. E 69(5), 057601 (2004).
[Crossref]

Chance, R. R.

R. R. Chance, A. Prock, and R. Silbey, Molecular Fluorescence and Energy Transfer Near Interfaces (John Wiley & Sons, Ltd, 2007), pp. 1–65.

Chao, P.

S. Molesky, P. Chao, and A. W. Rodriguez, “$\mathbb {T}$T operator bounds on electromagnetic power transfer: Application to far-field cross sections,” (2020). Https://arxiv.org/abs/2001.11531 .

Christensen, T.

O. D. Miller, O. Ilic, T. Christensen, M. T. H. Reid, H. A. Atwater, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Limits to the optical response of graphene and two-dimensional materials,” Nano Lett. 17(9), 5408–5415 (2017).
[Crossref]

Christiansen, R. E.

R. E. Christiansen, J. Michon, M. Benzaouia, O. Sigmund, and S. G. Johnson, “Inverse design of nanoparticles for enhanced raman scattering,” Opt. Express 28(4), 4444–4462 (2020).
[Crossref]

F. Wang, R. E. Christiansen, Y. Yu, J. Mørk, and O. Sigmund, “Maximizing the quality factor to mode volume ratio for ultra-small photonic crystal cavities,” Appl. Phys. Lett. 113(24), 241101 (2018).
[Crossref]

Cintra, S.

T. A. Kelf, Y. Sugawara, R. M. Cole, J. J. Baumberg, M. E. Abdelsalam, S. Cintra, S. Mahajan, A. E. Russell, and P. N. Bartlett, “Localized and delocalized plasmons in metallic nanovoids,” Phys. Rev. B 74(24), 245415 (2006).
[Crossref]

Cole, R. M.

T. A. Kelf, Y. Sugawara, R. M. Cole, J. J. Baumberg, M. E. Abdelsalam, S. Cintra, S. Mahajan, A. E. Russell, and P. N. Bartlett, “Localized and delocalized plasmons in metallic nanovoids,” Phys. Rev. B 74(24), 245415 (2006).
[Crossref]

Cormen, T. H.

T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms (MIT, Cambridge, 2009), 3rd ed.

D’Aguanno, G.

G. D’Aguanno, N. Mattiucci, M. Centini, M. Scalora, and M. J. Bloemer, “Electromagnetic density of modes for a finite-size three-dimensional structure,” Phys. Rev. E 69(5), 057601 (2004).
[Crossref]

de Abajo, F. J. G.

E. J. R. Vesseur, F. J. G. de Abajo, and A. Polman, “Broadband purcell enhancement in plasmonic ring cavities,” Phys. Rev. B 82(16), 165419 (2010).
[Crossref]

DeLacy, B. G.

O. D. Miller, A. G. Polimeridis, M. T. H. Reid, C. W. Hsu, B. G. DeLacy, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Fundamental limits to optical response in absorptive systems,” Opt. Express 24(4), 3329–3364 (2016).
[Crossref]

O. D. Miller, C. W. Hsu, M. T. H. Reid, W. Qiu, B. G. DeLacy, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Fundamental limits to extinction by metallic nanoparticles,” Phys. Rev. Lett. 112(12), 123903 (2014).
[Crossref]

Engquist, M.

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O. D. Miller, O. Ilic, T. Christensen, M. T. H. Reid, H. A. Atwater, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Limits to the optical response of graphene and two-dimensional materials,” Nano Lett. 17(9), 5408–5415 (2017).
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H. Shim, L. Fan, S. G. Johnson, and O. D. Miller, “Fundamental limits to near-field optical response over any bandwidth,” Phys. Rev. X 9(1), 011043 (2019).
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R. E. Christiansen, J. Michon, M. Benzaouia, O. Sigmund, and S. G. Johnson, “Inverse design of nanoparticles for enhanced raman scattering,” Opt. Express 28(4), 4444–4462 (2020).
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[Crossref]

O. D. Miller, A. G. Polimeridis, M. T. H. Reid, C. W. Hsu, B. G. DeLacy, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Fundamental limits to optical response in absorptive systems,” Opt. Express 24(4), 3329–3364 (2016).
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O. D. Miller, C. W. Hsu, M. T. H. Reid, W. Qiu, B. G. DeLacy, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Fundamental limits to extinction by metallic nanoparticles,” Phys. Rev. Lett. 112(12), 123903 (2014).
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R. E. Hamam, A. Karalis, J. D. Joannopoulos, and M. Soljačić, “Coupled-mode theory for general free-space resonant scattering of waves,” Phys. Rev. A 75(5), 053801 (2007).
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G. Strang, Computational Science and Engineering (Wellesley, 2007).

Sugawara, Y.

T. A. Kelf, Y. Sugawara, R. M. Cole, J. J. Baumberg, M. E. Abdelsalam, S. Cintra, S. Mahajan, A. E. Russell, and P. N. Bartlett, “Localized and delocalized plasmons in metallic nanovoids,” Phys. Rev. B 74(24), 245415 (2006).
[Crossref]

Suh, W.

W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40(10), 1511–1518 (2004).
[Crossref]

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N. P. van Dijk, K. Maute, M. Langelaar, and F. van Keulen, “Level-set methods for structural topology optimization: a review,” Struct. Multidisc. Optim. 48(3), 437–472 (2013).
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M. Heinkenschloss and L. N. Vicente, “Analysis of inexact trust-region sqp algorithms,” SIAM J. Optim. 12(2), 283–302 (2002).
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S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12(11), 659–670 (2018).
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F. Wang, R. E. Christiansen, Y. Yu, J. Mørk, and O. Sigmund, “Maximizing the quality factor to mode volume ratio for ultra-small photonic crystal cavities,” Appl. Phys. Lett. 113(24), 241101 (2018).
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W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40(10), 1511–1518 (2004).
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F. Wijnands, J. B. Pendry, F. J. Garcia-Vidal, P. M. Bell, P. J. Roberts, and L. M. Moreno, “Green’s functions for Maxwell’s equations: Application to spontaneous emission,” Opt. Quantum Electron. 29(2), 199–216 (1997).
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Y. Xu, R. K. Lee, and A. Yariv, “Quantum analysis and the classical analysis of spontaneous emission in a microcavity,” Phys. Rev. A 61(3), 033807 (2000).
[Crossref]

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J. Vučković, M. Pelton, A. Scherer, and Y. Yamamoto, “Optimization of three-dimensional micropost microcavities for cavity quantum electrodynamics,” Phys. Rev. A 66(2), 023808 (2002).
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Y. Xu, R. K. Lee, and A. Yariv, “Quantum analysis and the classical analysis of spontaneous emission in a microcavity,” Phys. Rev. A 61(3), 033807 (2000).
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F. Wang, R. E. Christiansen, Y. Yu, J. Mørk, and O. Sigmund, “Maximizing the quality factor to mode volume ratio for ultra-small photonic crystal cavities,” Appl. Phys. Lett. 113(24), 241101 (2018).
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A. Mazaheri, H. R. Fallah, and J. Zarbakhsh, “Application of ldos and multipole expansion technique in optimization of photonic crystal designs,” Opt. Quant. Electron. 45(1), 67–77 (2013).
[Crossref]

Zhang, L.

Z. Kuang, L. Zhang, and O. D. Miller, “Maximal single-frequency electromagnetic response,” (2020). Https://arxiv.org/abs/2002.00521 .

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F. Wang, R. E. Christiansen, Y. Yu, J. Mørk, and O. Sigmund, “Maximizing the quality factor to mode volume ratio for ultra-small photonic crystal cavities,” Appl. Phys. Lett. 113(24), 241101 (2018).
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M. T. H. Reid and S. G. Johnson, “Efficient computation of power, force, and torque in bem scattering calculations,” IEEE Trans. Antennas Propag. 63(8), 3588–3598 (2015).
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D. A. Tortorelli and P. Michaleris, “Design sensitivity analysis: Overview and review,” Inverse Probl. Eng. 1(1), 71–105 (1994).
[Crossref]

J. Phys.: Condens. Matter (1)

S. Raza, S. I. Bozhevolnyi, M. Wubs, and N. A. Mortensen, “Nonlocal optical response in metallic nanostructures,” J. Phys.: Condens. Matter 27(18), 183204 (2015).
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Nat. Photonics (2)

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12(11), 659–670 (2018).
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Opt. Express (5)

Opt. Quant. Electron. (1)

A. Mazaheri, H. R. Fallah, and J. Zarbakhsh, “Application of ldos and multipole expansion technique in optimization of photonic crystal designs,” Opt. Quant. Electron. 45(1), 67–77 (2013).
[Crossref]

Opt. Quantum Electron. (2)

F. Wijnands, J. B. Pendry, F. J. Garcia-Vidal, P. M. Bell, P. J. Roberts, and L. M. Moreno, “Green’s functions for Maxwell’s equations: Application to spontaneous emission,” Opt. Quantum Electron. 29(2), 199–216 (1997).
[Crossref]

F. Wijnands, J. B. Pendry, F. J. Garcia-Vidal, P. M. Bell, P. J. Roberts, and L. M. Moreno, “Green’s functions for maxwell’s equations: application to spontaneous emission,” Opt. Quantum Electron. 29(2), 199–216 (1997).
[Crossref]

Phys. Rev. A (3)

Y. Xu, R. K. Lee, and A. Yariv, “Quantum analysis and the classical analysis of spontaneous emission in a microcavity,” Phys. Rev. A 61(3), 033807 (2000).
[Crossref]

R. E. Hamam, A. Karalis, J. D. Joannopoulos, and M. Soljačić, “Coupled-mode theory for general free-space resonant scattering of waves,” Phys. Rev. A 75(5), 053801 (2007).
[Crossref]

J. Vučković, M. Pelton, A. Scherer, and Y. Yamamoto, “Optimization of three-dimensional micropost microcavities for cavity quantum electrodynamics,” Phys. Rev. A 66(2), 023808 (2002).
[Crossref]

Phys. Rev. B (4)

E. J. R. Vesseur, F. J. G. de Abajo, and A. Polman, “Broadband purcell enhancement in plasmonic ring cavities,” Phys. Rev. B 82(16), 165419 (2010).
[Crossref]

T. A. Kelf, Y. Sugawara, R. M. Cole, J. J. Baumberg, M. E. Abdelsalam, S. Cintra, S. Mahajan, A. E. Russell, and P. N. Bartlett, “Localized and delocalized plasmons in metallic nanovoids,” Phys. Rev. B 74(24), 245415 (2006).
[Crossref]

S. Molesky, P. S. Venkataram, W. Jin, and A. W. Rodriguez, “Fundamental limits to radiative heat transfer: Theory,” Phys. Rev. B 101(3), 035408 (2020).
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K. Joulain, R. Carminati, J.-P. Mulet, and J.-J. Greffet, “Definition and measurement of the local density of electromagnetic states close to an interface,” Phys. Rev. B 68(24), 245405 (2003).
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O. D. Miller, C. W. Hsu, M. T. H. Reid, W. Qiu, B. G. DeLacy, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Fundamental limits to extinction by metallic nanoparticles,” Phys. Rev. Lett. 112(12), 123903 (2014).
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Z. Ruan and S. Fan, “Superscattering of light from subwavelength nanostructures,” Phys. Rev. Lett. 105(1), 013901 (2010).
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H. Shim, L. Fan, S. G. Johnson, and O. D. Miller, “Fundamental limits to near-field optical response over any bandwidth,” Phys. Rev. X 9(1), 011043 (2019).
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M. Heinkenschloss and L. N. Vicente, “Analysis of inexact trust-region sqp algorithms,” SIAM J. Optim. 12(2), 283–302 (2002).
[Crossref]

Struct. Multidisc. Optim. (1)

N. P. van Dijk, K. Maute, M. Langelaar, and F. van Keulen, “Level-set methods for structural topology optimization: a review,” Struct. Multidisc. Optim. 48(3), 437–472 (2013).
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Supplementary Material (10)

NameDescription
» Visualization 1       Mesh file of optimized silver cavity for the polarized LDOS with polynomials at the wavelength 500 nm and minimum separation 50 nm
» Visualization 2       Mesh file of optimized silver cavity for the polarized LDOS with polynomials at the wavelength 500 nm and minimum separation 50 nm
» Visualization 3       Mesh file of optimized silver cavity for the polarized LDOS with polynomials at the wavelength 500 nm and minimum separation 50 nm
» Visualization 4       Mesh file of optimized silver cavity for the polarized LDOS with polynomials at the wavelength 500 nm and minimum separation 50 nm
» Visualization 5       Mesh file of optimized silver cavity for the polarized LDOS with polynomials at the wavelength 600 nm and minimum separation 50 nm
» Visualization 6       Mesh file of optimized silver cavity for the polarized LDOS with polynomials at the wavelength 700 nm and minimum separation 50 nm
» Visualization 7       Mesh file of optimized silver cavity for the polarized LDOS with cylinder at the wavelength 400 nm and minimum separation 50 nm
» Visualization 8       Mesh file of optimized silver cavity for the polarized LDOS with cylinder at the wavelength 500 nm and minimum separation 50 nm
» Visualization 9       Mesh file of optimized silver cavity for the polarized LDOS with cylinder at the wavelength 600 nm and minimum separation 50 nm
» Visualization 10       Mesh file of optimized silver cavity for the polarized LDOS with cylinder at the wavelength 700 nm and minimum separation 50 nm

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Figures (5)

Fig. 1.
Fig. 1. Schematic cavity-optimization problem: the shape of an air cavity in a metallic (silver) background is optimized to maximize the LDOS for emitters (dipoles) at the center $o$, constrained for a minimum separation $d$ (the metal lies outside of a sphere of radius $d$).
Fig. 2.
Fig. 2. (a) Total LDOS optima as a function of the wavelength $\lambda$ for a minimum separation $d=50$ nm, along with the upper bound (black line). A separately optimized structure is used for each wavelength, either optimized cylinders (orange line) and ellipsoids (green line) or general shape optimization via the optimized spherical-harmonic (SH) surfaces (blue dots) of Eq. (3). Several SH local optima are shown for each $\lambda$, whereas for cylinders and ellipsoids only the global optima are shown. (b) LDOS spectra of the spherical-harmonic (blue) and cylinder (orange) structures optimized for $\lambda =500$ nm, the the shapes (not to scale) inset (see supplementary Visualization 1 and Visualization 2 for 3D views). Also shown is the total-LDOS spectrum of a polynomial shape (dashed blue line) optimized for the polarized LDOS in Sec. 4.2, showing that optimizing for a single dipole orientation (polarized LDOS) is nearly equivalent in performance to optimizing for all orientations (total LDOS).
Fig. 3.
Fig. 3. (a) Polarized LDOS optima (dashed lines) as a function of the wavelength $\lambda$ at a minimum separation $d=50$ nm, along with the upper bound (black line) and the shape-dependent bounds (black dots). Dashed lines are peak performance of separately optimized structures for each $\lambda$, either cylinders (orange) or the optimized polynomials (blue) of Eq. (4). Solid blue lines are spectra of the polarized LDOS for optimized polynomial designs at selected wavelengths $\lambda = 400, 500, 600, 700, 800$ nm, respectively. (b) Optimized polynomial (top) and cylinder (bottom) structures at the wavelength $\lambda = 400, 500, 600, 700$ nm (to scale; see supplementary Visualization 3, Visualization 4, Visualization 5, Visualization 6, Visualization 7, Visualization 8, Visualization 9, and Visualization 10 for 3D views).
Fig. 4.
Fig. 4. LDOS of a resonant air sphere in silver as a function of the wavelength $\lambda$ (blue line), where for each $\lambda$ we choose the smallest radius $a_{\mathrm {res}}$ for which we couple to a resonant mode at $\lambda$. The black line is the corresponding upper bound from Eq. (7), setting the minimum separation distance $d = a_{\mathrm {res}}$. The LDOS slightly exceeds the bound at small wavelengths where the radius becomes so large that one would need to include the $\mathrm {O}(kL)$ term that we dropped in Eq. (6).
Fig. 5.
Fig. 5. LDOS of optimized cylindrical cavity a function of the wall thickness (blue line) at a wavelength $\lambda =500$ nm and a minimum separation $d=50$ nm, compared to the infinite-thickness LDOS (orange line). Also shown are the radiative LDOS $\rho _{\mathrm {rad}}/\rho _0$ (solid green line: the radiated/non-absorbed power), as well as $4\times \rho _{\mathrm {rad}}/\rho _0$ (dashed green line) because the theoretical bounds predict that the maximum $\rho _{\mathrm {rad}}$ is $1/4$ of the total LDOS [1].

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

ρ = Im [ ϵ 0 π ω j = 1 3 s ^ j E j ( x 0 ) ] ,
ρ ρ 0 1 + | χ ( ω ) | 2 Im χ ( ω ) [ 1 ( k d ) 3 + 1 k d ] .
R ( θ , ϕ ) = d + | n = 0 N c n S n ( θ , ϕ ) | 2 .
S n ( θ , ϕ ) = { θ n θ π 2 , ( π θ ) n θ > π 2 .
ρ ρ 0 1 + k 3 4 π | χ ( ω ) | 2 Im χ ( ω ) V [ 3 ( k r ) 6 + 1 ( k r ) 4 + 1 ( k r ) 2 ] d 3 r ,
ρ ρ 0 1 + | χ ( ω ) | 2 Im χ ( ω ) [ 1 ( k d ) 3 + 1 k d + O ( k L ) ] ,
ρ ρ 0 1 + | χ ( ω ) | 2 Im χ ( ω ) [ 1 ( k d ) 3 + 1 k d ] .
ρ p ρ 0 1 3 + k 3 8 π | χ ( ω ) | 2 Im χ ( ω ) V [ a ( r ) + b ( r ) | p ^ r ^ | 2 ] d 3 r ,
a ( r ) = 1 ( k r ) 6 1 ( k r ) 4 + 1 ( k r ) 2
b ( r ) = 3 ( k r ) 6 + 5 ( k r ) 4 1 ( k r ) 2 .
ρ p ρ 0 1 3 + | χ ( ω ) | 2 3 Im χ ( ω ) [ 1 ( k d ) 3 + 1 k d ] ,
δ F = 2 Re Ω δ R ( x ) [ ( 1 ε ) E ( x ) E A ( x ) + ( 1 ε 1 ) D ( x ) D A ( x ) ] d S ,
ρ = Im [ ϵ 0 π ω j = 1 3 s ^ j E j ( x 0 ) ] ,
E j A ( x ) = Im [ ϵ 0 π ω E j ] .
δ ρ = ϵ 0 π ω Im j Ω δ R ( x ) [ ( 1 ε ) E j ( x ) 2 + ( 1 ε 1 ) D j ( x ) 2 ] d S .
ϵ m ( ω ) H ( k m a ) [ k d a J ( k d a ) ] = ϵ d J ( k d a ) [ k m a H ( k m a ) ] ,
Q 2 V Q r = Q a 2 Q r ( Q a + Q r ) 2 V .